Chapter 13.3, Problem 59ES

The volume V of a right circular cylinder is given by the formula $V=\pi r^{2}h,$ where r is the radius and h is the height.

(a) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remains constant.

(b) Find a formula for the instantaneous rate of change of V with respect to h if h changes and r remains constant.

(c) Suppose that h has a constant value of 4 in, but r varies. Find the rate of change of V with respect to r at the point where $r=6$ in.

(d) Suppose that r has a constant value of 8 in, but h varies. Find the instantaneous rate of change of V with respect to h at the point where $h=10.$ in